%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV482^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:21 AM UTC 2026
% Result : Theorem 1.34s 1.24s
% Output : Refutation 1.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV482^1 : TPTP v9.2.1. Released v7.0.0.
% 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n026.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 12:47:55 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.38 ---- Original DTF file ---
% 0.14/0.38 thf(spec,logic,$$dhol).
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 % File : SEV482^1 : TPTP v9.2.1. Released v7.0.0.
% 0.14/0.38 % Domain : Analysis
% 0.14/0.38 % Problem : FORALL_IN_CROSS
% 0.14/0.38 % Version : Especial.
% 0.14/0.38 % English :
% 0.14/0.38
% 0.14/0.38 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.14/0.38 % Source : [Kal16]
% 0.14/0.38 % Names : FORALL_IN_CROSS_.p [Kal16]
% 0.14/0.38
% 0.14/0.38 % Status : Theorem
% 0.14/0.38 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.14/0.38 % Syntax : Number of formulae : 7 ( 3 unt; 4 typ; 0 def)
% 0.14/0.38 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.14/0.38 % Maximal formula atoms : 1 ( 3 avg)
% 0.14/0.38 % Number of connectives : 62 ( 0 ~; 0 |; 2 &; 58 @)
% 0.14/0.38 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.14/0.38 % Maximal formula depth : 7 ( 6 avg)
% 0.14/0.38 % Number of types : 1 ( 0 usr)
% 0.14/0.38 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.14/0.38 % Number of symbols : 5 ( 4 usr; 0 con; 2-5 aty)
% 0.14/0.38 % Number of variables : 25 ( 0 ^; 20 !; 0 ?; 25 :)
% 0.14/0.38 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.14/0.38 % SPC : TH1_THM_EQU_NAR
% 0.14/0.38
% 0.14/0.38 % Comments : Exported from core HOL Light.
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 thf('thf_type_type/pair/prod',type,
% 0.14/0.38 'type/pair/prod': $tType > $tType > $tType ).
% 0.14/0.38
% 0.14/0.38 thf('thf_const_const/sets/IN',type,
% 0.14/0.38 'const/sets/IN':
% 0.14/0.38 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf('thf_const_const/sets/CROSS',type,
% 0.14/0.38 'const/sets/CROSS':
% 0.14/0.38 !>[A: $tType,A0: $tType] : ( ( A > $o ) > ( A0 > $o ) > ( 'type/pair/prod' @ A @ A0 ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf('thf_const_const/pair/,',type,
% 0.14/0.38 'const/pair/,':
% 0.14/0.38 !>[A: $tType,B: $tType] : ( A > B > ( 'type/pair/prod' @ A @ B ) ) ).
% 0.14/0.38
% 0.14/0.38 thf('thm/sets/IN_CROSS_',axiom,
% 0.14/0.38 ! [A: $tType,A0: $tType,A1: A,A2: A0,A3: A > $o,A4: A0 > $o] :
% 0.14/0.38 ( ( 'const/sets/IN' @ ( 'type/pair/prod' @ A @ A0 ) @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) @ ( 'const/sets/CROSS' @ A @ A0 @ A3 @ A4 ) )
% 0.14/0.38 = ( ( 'const/sets/IN' @ A @ A1 @ A3 )
% 0.14/0.38 & ( 'const/sets/IN' @ A0 @ A2 @ A4 ) ) ) ).
% 0.14/0.38
% 0.14/0.38 thf('thm/pair/FORALL_PAIR_THM_',axiom,
% 0.14/0.38 ! [A: $tType,A0: $tType,P: ( 'type/pair/prod' @ A @ A0 ) > $o] :
% 0.14/0.38 ( ( ! [A1: 'type/pair/prod' @ A @ A0] : ( P @ A1 ) )
% 0.14/0.38 = ( ! [A1: A,A2: A0] : ( P @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 thf('thm/sets/FORALL_IN_CROSS_',conjecture,
% 0.14/0.38 ! [A: $tType,A0: $tType,P: ( 'type/pair/prod' @ A @ A0 ) > $o,A1: A > $o,A2: A0 > $o] :
% 0.14/0.38 ( ( ! [A3: 'type/pair/prod' @ A @ A0] :
% 0.14/0.38 ( ( 'const/sets/IN' @ ( 'type/pair/prod' @ A @ A0 ) @ A3 @ ( 'const/sets/CROSS' @ A @ A0 @ A1 @ A2 ) )
% 0.14/0.38 => ( P @ A3 ) ) )
% 0.14/0.38 = ( ! [A3: A,A4: A0] :
% 0.14/0.38 ( ( ( 'const/sets/IN' @ A @ A3 @ A1 )
% 0.14/0.38 & ( 'const/sets/IN' @ A0 @ A4 @ A2 ) )
% 0.14/0.38 => ( P @ ( 'const/pair/,' @ A @ A0 @ A3 @ A4 ) ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 ------------------------
% 1.20/1.09 ---- Embedded in THF ---
% 1.20/1.09 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.20/1.09 %%% Generated on Tue Feb 24 12:47:55 EST 2026
% 1.20/1.09 %%% using '$$dhol' embedding, version 1.3.0.
% 1.20/1.09 %%% Logic specification used:
% 1.20/1.09 %%% thf(spec, logic, $$dhol).
% 1.20/1.09
% 1.20/1.09 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UBNaezbv7d/DTF2DTF10777.p
% 1.20/1.09 thf('thf_type_type/pair/prod', type, 'type/pair/prod': ($tType > ($tType > $tType))).
% 1.20/1.09 thf('thf_const_const/sets/IN', type, 'const/sets/IN': (!> [A:$tType]: ((A > ((A > $o) > $o))))).
% 1.20/1.09 thf('thf_const_const/sets/CROSS', type, 'const/sets/CROSS': (!> [A:$tType,A0:$tType]: (((A > $o) > ((A0 > $o) > ((('type/pair/prod' @ A) @ A0) > $o)))))).
% 1.20/1.09 thf('thf_const_const/pair/,', type, 'const/pair/,': (!> [A:$tType,B:$tType]: ((A > (B > (('type/pair/prod' @ A) @ B)))))).
% 1.20/1.09 thf('thm/sets/IN_CROSS_', axiom, (! [A:$tType,A0:$tType,A1:A,A2:A0,A3:(A > $o),A4:(A0 > $o)]: ((((('const/sets/IN' @ (('type/pair/prod' @ A) @ A0)) @ (((('const/pair/,' @ A) @ A0) @ A1) @ A2)) @ (((('const/sets/CROSS' @ A) @ A0) @ A3) @ A4)) = (((('const/sets/IN' @ A) @ A1) @ A3) & ((('const/sets/IN' @ A0) @ A2) @ A4)))))).
% 1.20/1.09 thf('thm/pair/FORALL_PAIR_THM_', axiom, (! [A:$tType,A0:$tType,P:((('type/pair/prod' @ A) @ A0) > $o)]: (((! [A1:(('type/pair/prod' @ A) @ A0)]: ((P @ A1))) = (! [A1:A,A2:A0]: ((P @ (((('const/pair/,' @ A) @ A0) @ A1) @ A2)))))))).
% 1.20/1.09 thf('thm/sets/FORALL_IN_CROSS_', conjecture, (! [A:$tType,A0:$tType,P:((('type/pair/prod' @ A) @ A0) > $o),A1:(A > $o),A2:(A0 > $o)]: (((! [A3:(('type/pair/prod' @ A) @ A0)]: ((((('const/sets/IN' @ (('type/pair/prod' @ A) @ A0)) @ A3) @ (((('const/sets/CROSS' @ A) @ A0) @ A1) @ A2)) => (P @ A3)))) = (! [A3:A,A4:A0]: (((((('const/sets/IN' @ A) @ A3) @ A1) & ((('const/sets/IN' @ A0) @ A4) @ A2)) => (P @ (((('const/pair/,' @ A) @ A0) @ A3) @ A4))))))))).
% 1.20/1.09 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UBNaezbv7d/DTF2DTF10777.p
% 1.20/1.09 ------------------------
% 1.20/1.10 ---- Cleaned THF ---
% 1.20/1.10 thf('thf_type_type/pair/prod',type,
% 1.20/1.10 'type/pair/prod': $tType > $tType > $tType ).
% 1.20/1.10
% 1.20/1.10 thf('thf_const_const/sets/IN',type,
% 1.20/1.10 'const/sets/IN':
% 1.20/1.10 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.20/1.10
% 1.20/1.10 thf('thf_const_const/sets/CROSS',type,
% 1.20/1.10 'const/sets/CROSS':
% 1.20/1.10 !>[A: $tType,A0: $tType] : ( ( A > $o ) > ( A0 > $o ) > ( 'type/pair/prod' @ A @ A0 ) > $o ) ).
% 1.20/1.10
% 1.20/1.10 thf('thf_const_const/pair/,',type,
% 1.20/1.10 'const/pair/,':
% 1.20/1.10 !>[A: $tType,B: $tType] : ( A > B > ( 'type/pair/prod' @ A @ B ) ) ).
% 1.20/1.10
% 1.20/1.10 thf('thm/sets/IN_CROSS_',axiom,
% 1.20/1.10 ! [A: $tType,A0: $tType,A1: A,A2: A0,A3: A > $o,A4: A0 > $o] :
% 1.20/1.10 ( ( 'const/sets/IN' @ ( 'type/pair/prod' @ A @ A0 ) @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) @ ( 'const/sets/CROSS' @ A @ A0 @ A3 @ A4 ) )
% 1.20/1.10 = ( ( 'const/sets/IN' @ A @ A1 @ A3 )
% 1.20/1.10 & ( 'const/sets/IN' @ A0 @ A2 @ A4 ) ) ) ).
% 1.20/1.10
% 1.20/1.10 thf('thm/pair/FORALL_PAIR_THM_',axiom,
% 1.20/1.10 ! [A: $tType,A0: $tType,P: ( 'type/pair/prod' @ A @ A0 ) > $o] :
% 1.20/1.10 ( ( ! [A1: 'type/pair/prod' @ A @ A0] : ( P @ A1 ) )
% 1.20/1.10 = ( ! [A1: A,A2: A0] : ( P @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) ) ) ) ).
% 1.20/1.10
% 1.20/1.10 thf('thm/sets/FORALL_IN_CROSS_',conjecture,
% 1.20/1.10 ! [A: $tType,A0: $tType,P: ( 'type/pair/prod' @ A @ A0 ) > $o,A1: A > $o,A2: A0 > $o] :
% 1.20/1.10 ( ( ! [A3: 'type/pair/prod' @ A @ A0] :
% 1.20/1.10 ( ( 'const/sets/IN' @ ( 'type/pair/prod' @ A @ A0 ) @ A3 @ ( 'const/sets/CROSS' @ A @ A0 @ A1 @ A2 ) )
% 1.20/1.10 => ( P @ A3 ) ) )
% 1.20/1.10 = ( ! [A3: A,A4: A0] :
% 1.20/1.10 ( ( ( 'const/sets/IN' @ A @ A3 @ A1 )
% 1.20/1.10 & ( 'const/sets/IN' @ A0 @ A4 @ A2 ) )
% 1.20/1.10 => ( P @ ( 'const/pair/,' @ A @ A0 @ A3 @ A4 ) ) ) ) ) ).
% 1.20/1.10 ------------------------
% 1.20/1.11 % (10875)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/183Mi)
% 1.20/1.12 % (10876)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/4Mi)
% 1.20/1.12 % (10879)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/2Mi)
% 1.20/1.12 % (10877)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/27Mi)
% 1.20/1.12 % (10878)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/2Mi)
% 1.20/1.12 % (10880)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/275Mi)
% 1.20/1.12 % (10881)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10777 for (3000ds/18Mi)
% 1.20/1.12 % Exception at run slice level
% 1.20/1.12 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.20/1.12 % (10876)Instruction limit reached!
% 1.20/1.12 % (10876)------------------------------
% 1.20/1.12 % (10876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.20/1.12 % (10876)Termination reason: Unknown
% 1.20/1.12 % (10876)Termination phase: Saturation
% 1.20/1.12
% 1.20/1.12 % (10876)Memory used [KB]: 5500
% 1.20/1.12 % (10876)Time elapsed: 0.003 s
% 1.20/1.12 % (10876)Instructions burned: 4 (million)
% 1.20/1.12 % (10876)------------------------------
% 1.20/1.12 % (10876)------------------------------
% 1.20/1.12 % (10878)Instruction limit reached!
% 1.20/1.12 % (10878)------------------------------
% 1.20/1.12 % (10878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.20/1.12 % (10878)Termination reason: Unknown
% 1.20/1.12 % (10878)Termination phase: Saturation
% 1.20/1.12
% 1.20/1.12 % (10878)Memory used [KB]: 5500
% 1.20/1.12 % (10878)Time elapsed: 0.003 s
% 1.20/1.12 % (10878)Instructions burned: 3 (million)
% 1.20/1.12 % (10878)------------------------------
% 1.20/1.12 % (10878)------------------------------
% 1.20/1.12 % (10880)Refutation not found, incomplete strategy
% 1.20/1.12 % (10880)------------------------------
% 1.20/1.12 % (10880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.20/1.12 % (10880)Termination reason: Refutation not found, incomplete strategy
% 1.20/1.12
% 1.20/1.12
% 1.20/1.12 % (10880)Memory used [KB]: 5628
% 1.20/1.12 % (10880)Time elapsed: 0.005 s
% 1.20/1.12 % (10880)Instructions burned: 6 (million)
% 1.20/1.12 % (10880)------------------------------
% 1.20/1.12 % (10880)------------------------------
% 1.34/1.13 % (10881)Instruction limit reached!
% 1.34/1.13 % (10881)------------------------------
% 1.34/1.13 % (10881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.13 % (10881)Termination reason: Unknown
% 1.34/1.13 % (10881)Termination phase: Saturation
% 1.34/1.13
% 1.34/1.13 % (10881)Memory used [KB]: 5628
% 1.34/1.13 % (10881)Time elapsed: 0.011 s
% 1.34/1.13 % (10881)Instructions burned: 19 (million)
% 1.34/1.13 % (10881)------------------------------
% 1.34/1.13 % (10881)------------------------------
% 1.34/1.13 % (10877)Instruction limit reached!
% 1.34/1.13 % (10877)------------------------------
% 1.34/1.13 % (10877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.13 % (10877)Termination reason: Unknown
% 1.34/1.13 % (10877)Termination phase: Saturation
% 1.34/1.13
% 1.34/1.13 % (10877)Memory used [KB]: 5628
% 1.34/1.13 % (10877)Time elapsed: 0.016 s
% 1.34/1.13 % (10877)Instructions burned: 27 (million)
% 1.34/1.13 % (10877)------------------------------
% 1.34/1.13 % (10877)------------------------------
% 1.34/1.13 % (10882)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/3Mi)
% 1.34/1.13 % (10883)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/37Mi)
% 1.34/1.13 % (10884)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/15Mi)
% 1.34/1.13 % Exception at run slice level
% 1.34/1.13 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.13 % (10882)Instruction limit reached!
% 1.34/1.13 % (10882)------------------------------
% 1.34/1.13 % (10882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.13 % (10882)Termination reason: Unknown
% 1.34/1.13 % (10882)Termination phase: Saturation
% 1.34/1.13
% 1.34/1.13 % (10882)Memory used [KB]: 5500
% 1.34/1.13 % (10882)Time elapsed: 0.003 s
% 1.34/1.13 % (10882)Instructions burned: 3 (million)
% 1.34/1.13 % (10882)------------------------------
% 1.34/1.13 % (10882)------------------------------
% 1.34/1.14 % (10885)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/3Mi)
% 1.34/1.14 % (10885)Instruction limit reached!
% 1.34/1.14 % (10885)------------------------------
% 1.34/1.14 % (10885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.14 % (10885)Termination reason: Unknown
% 1.34/1.14 % (10885)Termination phase: Saturation
% 1.34/1.14
% 1.34/1.14 % (10885)Memory used [KB]: 5500
% 1.34/1.14 % (10885)Time elapsed: 0.003 s
% 1.34/1.14 % (10885)Instructions burned: 3 (million)
% 1.34/1.14 % (10885)------------------------------
% 1.34/1.14 % (10885)------------------------------
% 1.34/1.14 % (10886)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/1041Mi)
% 1.34/1.14 % Exception at run slice level% (10884)Instruction limit reached!
% 1.34/1.14 % (10884)------------------------------
% 1.34/1.14 % (10884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.14
% 1.34/1.14 % (10884)Termination reason: Unknown
% 1.34/1.14 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire% (10884)Termination phase: Saturation
% 1.34/1.14
% 1.34/1.14
% 1.34/1.14 % (10884)Memory used [KB]: 5756
% 1.34/1.14 % (10884)Time elapsed: 0.010 s
% 1.34/1.14 % (10884)Instructions burned: 16 (million)
% 1.34/1.14 % (10884)------------------------------
% 1.34/1.14 % (10884)------------------------------
% 1.34/1.15 % (10887)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/7Mi)
% 1.34/1.15 % (10888)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/16Mi)
% 1.34/1.15 % (10889)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/3Mi)
% 1.34/1.15 % (10887)Instruction limit reached!
% 1.34/1.15 % (10887)------------------------------
% 1.34/1.15 % (10887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.15 % (10887)Termination reason: Unknown
% 1.34/1.15 % (10887)Termination phase: Saturation
% 1.34/1.15
% 1.34/1.15 % (10887)Memory used [KB]: 1023
% 1.34/1.15 % (10887)Time elapsed: 0.005 s
% 1.34/1.15 % (10887)Instructions burned: 7 (million)
% 1.34/1.15 % (10887)------------------------------
% 1.34/1.15 % (10887)------------------------------
% 1.34/1.15 % (10889)Instruction limit reached!
% 1.34/1.15 % (10889)------------------------------
% 1.34/1.15 % (10889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.15 % (10889)Termination reason: Unknown
% 1.34/1.15 % (10889)Termination phase: Saturation
% 1.34/1.15
% 1.34/1.15 % (10889)Memory used [KB]: 5500
% 1.34/1.15 % (10889)Time elapsed: 0.003 s
% 1.34/1.15 % (10889)Instructions burned: 4 (million)
% 1.34/1.15 % (10889)------------------------------
% 1.34/1.15 % (10889)------------------------------
% 1.34/1.15 % (10890)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/3Mi)
% 1.34/1.16 % (10890)Instruction limit reached!
% 1.34/1.16 % (10890)------------------------------
% 1.34/1.16 % (10890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.16 % (10890)Termination reason: Unknown
% 1.34/1.16 % (10890)Termination phase: Saturation
% 1.34/1.16
% 1.34/1.16 % (10890)Memory used [KB]: 1023
% 1.34/1.16 % (10890)Time elapsed: 0.003 s
% 1.34/1.16 % (10890)Instructions burned: 4 (million)
% 1.34/1.16 % (10890)------------------------------
% 1.34/1.16 % (10890)------------------------------
% 1.34/1.16 % (10891)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/7Mi)
% 1.34/1.16 % (10892)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/3Mi)
% 1.34/1.16 % (10888)Instruction limit reached!
% 1.34/1.16 % (10888)------------------------------
% 1.34/1.16 % (10888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.16 % (10888)Termination reason: Unknown
% 1.34/1.16 % (10888)Termination phase: Saturation
% 1.34/1.16
% 1.34/1.16 % (10888)Memory used [KB]: 5756
% 1.34/1.16 % (10888)Time elapsed: 0.010 s
% 1.34/1.16 % (10888)Instructions burned: 16 (million)
% 1.34/1.16 % (10888)------------------------------
% 1.34/1.16 % (10888)------------------------------
% 1.34/1.16 % Exception at run slice level
% 1.34/1.16 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.16 % (10891)Refutation not found, incomplete strategy
% 1.34/1.16 % (10891)------------------------------
% 1.34/1.16 % (10891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.16 % (10891)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.16
% 1.34/1.16
% 1.34/1.16 % (10891)Memory used [KB]: 5500
% 1.34/1.16 % (10891)Time elapsed: 0.003 s
% 1.34/1.16 % (10891)Instructions burned: 4 (million)
% 1.34/1.16 % (10891)------------------------------
% 1.34/1.16 % (10891)------------------------------
% 1.34/1.16 % (10875)Instruction limit reached!
% 1.34/1.16 % (10875)------------------------------
% 1.34/1.16 % (10875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.16 % (10875)Termination reason: Unknown
% 1.34/1.16 % (10875)Termination phase: Saturation
% 1.34/1.16
% 1.34/1.16 % (10875)Memory used [KB]: 6524
% 1.34/1.16 % (10875)Time elapsed: 0.056 s
% 1.34/1.16 % (10875)Instructions burned: 186 (million)
% 1.34/1.16 % (10875)------------------------------
% 1.34/1.16 % (10875)------------------------------
% 1.34/1.17 % (10893)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/4Mi)
% 1.34/1.17 % (10894)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/18Mi)
% 1.34/1.17 % (10893)Instruction limit reached!
% 1.34/1.17 % (10893)------------------------------
% 1.34/1.17 % (10893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.17 % (10893)Termination reason: Unknown
% 1.34/1.17 % (10893)Termination phase: Saturation
% 1.34/1.17
% 1.34/1.17 % (10893)Memory used [KB]: 5500
% 1.34/1.17 % (10893)Time elapsed: 0.003 s
% 1.34/1.17 % (10893)Instructions burned: 4 (million)
% 1.34/1.17 % (10893)------------------------------
% 1.34/1.17 % (10893)------------------------------
% 1.34/1.17 % (10895)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/710Mi)
% 1.34/1.17 % (10896)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/6Mi)
% 1.34/1.17 % (10897)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/902Mi)
% 1.34/1.17 % (10899)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/5Mi)
% 1.34/1.17 % Exception at run slice level
% 1.34/1.17 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.18 % (10898)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/21Mi)
% 1.34/1.18 % (10896)Instruction limit reached!
% 1.34/1.18 % (10896)------------------------------
% 1.34/1.18 % (10896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.18 % (10896)Termination reason: Unknown
% 1.34/1.18 % (10896)Termination phase: Saturation
% 1.34/1.18
% 1.34/1.18 % (10896)Memory used [KB]: 5500
% 1.34/1.18 % (10896)Time elapsed: 0.004 s
% 1.34/1.18 % (10896)Instructions burned: 6 (million)
% 1.34/1.18 % (10896)------------------------------
% 1.34/1.18 % (10896)------------------------------
% 1.34/1.18 % (10894)Instruction limit reached!
% 1.34/1.18 % (10894)------------------------------
% 1.34/1.18 % (10894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.18 % (10894)Termination reason: Unknown
% 1.34/1.18 % (10894)Termination phase: Saturation
% 1.34/1.18
% 1.34/1.18 % (10894)Memory used [KB]: 5628
% 1.34/1.18 % (10894)Time elapsed: 0.011 s
% 1.34/1.18 % (10894)Instructions burned: 18 (million)
% 1.34/1.18 % (10894)------------------------------
% 1.34/1.18 % (10894)------------------------------
% 1.34/1.18 % (10897)Refutation not found, incomplete strategy
% 1.34/1.18 % (10897)------------------------------
% 1.34/1.18 % (10897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.18 % (10897)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.18
% 1.34/1.18
% 1.34/1.18 % (10897)Memory used [KB]: 5500
% 1.34/1.18 % (10897)Time elapsed: 0.004 s
% 1.34/1.18 % (10897)Instructions burned: 5 (million)
% 1.34/1.18 % (10897)------------------------------
% 1.34/1.18 % (10897)------------------------------
% 1.34/1.18 % (10900)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/6Mi)
% 1.34/1.18 % (10901)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/377Mi)
% 1.34/1.18 % Exception at run slice level
% 1.34/1.18 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.19 % (10898)Instruction limit reached!
% 1.34/1.19 % (10898)------------------------------
% 1.34/1.19 % (10898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.19 % (10898)Termination reason: Unknown
% 1.34/1.19 % (10898)Termination phase: Saturation
% 1.34/1.19
% 1.34/1.19 % (10898)Memory used [KB]: 5628
% 1.34/1.19 % (10898)Time elapsed: 0.013 s
% 1.34/1.19 % (10898)Instructions burned: 22 (million)
% 1.34/1.19 % (10898)------------------------------
% 1.34/1.19 % (10898)------------------------------
% 1.34/1.19 % (10902)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/779Mi)
% 1.34/1.19 % (10903)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/19Mi)
% 1.34/1.19 % Exception at run slice level
% 1.34/1.19 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.19 % (10904)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/879Mi)
% 1.34/1.19 % Exception at run slice level
% 1.34/1.19 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.20 % (10905)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/17Mi)
% 1.34/1.20 % (10906)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/3Mi)
% 1.34/1.21 % (10906)Instruction limit reached!
% 1.34/1.21 % (10906)------------------------------
% 1.34/1.21 % (10906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (10906)Termination reason: Unknown
% 1.34/1.21 % (10906)Termination phase: Saturation
% 1.34/1.21
% 1.34/1.21 % (10906)Memory used [KB]: 1023
% 1.34/1.21 % (10906)Time elapsed: 0.003 s
% 1.34/1.21 % (10906)Instructions burned: 4 (million)
% 1.34/1.21 % (10906)------------------------------
% 1.34/1.21 % (10906)------------------------------
% 1.34/1.21 % (10908)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/127Mi)
% 1.34/1.21 % (10905)Instruction limit reached!
% 1.34/1.21 % (10905)------------------------------
% 1.34/1.21 % (10905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.21 % (10905)Termination reason: Unknown
% 1.34/1.21 % (10905)Termination phase: Saturation
% 1.34/1.21
% 1.34/1.21 % (10905)Memory used [KB]: 5628
% 1.34/1.21 % (10905)Time elapsed: 0.010 s
% 1.34/1.21 % (10905)Instructions burned: 18 (million)
% 1.34/1.21 % (10905)------------------------------
% 1.34/1.21 % (10905)------------------------------
% 1.34/1.22 % (10907)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/30Mi)
% 1.34/1.22 % (10909)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10777 for (2999ds/100Mi)
% 1.34/1.23 % (10910)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_10777 for (2998ds/3Mi)
% 1.34/1.23 % Exception at run slice level
% 1.34/1.23 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.34/1.23 % (10907)Instruction limit reached!
% 1.34/1.23 % (10907)------------------------------
% 1.34/1.23 % (10907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.23 % (10907)Termination reason: Unknown
% 1.34/1.23 % (10907)Termination phase: Saturation
% 1.34/1.23
% 1.34/1.23 % (10907)Memory used [KB]: 5628
% 1.34/1.23 % (10907)Time elapsed: 0.038 s
% 1.34/1.23 % (10907)Instructions burned: 31 (million)
% 1.34/1.23 % (10907)------------------------------
% 1.34/1.23 % (10907)------------------------------
% 1.34/1.23 % (10904)First to succeed.
% 1.34/1.24 % (10904)Refutation found. Thanks to Tanya!
% 1.34/1.24 % SZS status Theorem for DTF2THF_10777
% 1.34/1.24 % SZS output start Proof for DTF2THF_10777
% 1.34/1.24 thf(type_def_6, type, 'type/pair/prod': ($tType * $tType) > $tType).
% 1.34/1.24 thf(type_def_7, type, sK0: $tType).
% 1.34/1.24 thf(type_def_8, type, sK1: $tType).
% 1.34/1.24 thf(func_def_0, type, 'type/pair/prod': ($tType * $tType) > $tType).
% 1.34/1.24 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.34/1.24 thf(func_def_2, type, 'const/sets/CROSS': !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > 'type/pair/prod' @ X0 @ X1 > $o)).
% 1.34/1.24 thf(func_def_3, type, 'const/pair/,': !>[X0: $tType, X1: $tType]:(X0 > X1 > 'type/pair/prod' @ X0 @ X1)).
% 1.34/1.24 thf(func_def_13, type, sK2: 'type/pair/prod' @ sK0 @ sK1 > $o).
% 1.34/1.24 thf(func_def_14, type, sK3: sK0 > $o).
% 1.34/1.24 thf(func_def_15, type, sK4: sK1 > $o).
% 1.34/1.24 thf(func_def_17, type, sK6: 'type/pair/prod' @ sK0 @ sK1).
% 1.34/1.24 thf(func_def_18, type, sK7: sK1).
% 1.34/1.24 thf(func_def_19, type, sK8: sK0).
% 1.34/1.24 thf(func_def_20, type, sK9: !>[X0: $tType, X1: $tType]:(('type/pair/prod' @ X0 @ X1 > $o) > X1)).
% 1.34/1.24 thf(func_def_21, type, sK10: !>[X0: $tType, X1: $tType]:(('type/pair/prod' @ X0 @ X1 > $o) > X0)).
% 1.34/1.24 thf(func_def_22, type, sK11: !>[X0: $tType, X1: $tType]:(('type/pair/prod' @ X0 @ X1 > $o) > 'type/pair/prod' @ X0 @ X1)).
% 1.34/1.24 thf(func_def_24, type, ph12: !>[X0: $tType]:(X0)).
% 1.34/1.24 thf(f327,plain,(
% 1.34/1.24 $false),
% 1.34/1.24 inference(avatar_sat_refutation,[status(thm)],[f69,f78,f83,f88,f93,f94,f95,f290,f308,f326])).
% 1.34/1.24 thf(f326,plain,(
% 1.34/1.24 ~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_7),
% 1.34/1.24 inference(avatar_contradiction_clause,[status(thm)],[f325])).
% 1.34/1.24 thf(f325,plain,(
% 1.34/1.24 $false | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_7)),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f324])).
% 1.34/1.24 thf(f324,plain,(
% 1.34/1.24 ($false = $true) | (~spl5_1 | ~spl5_4 | ~spl5_6 | ~spl5_7)),
% 1.34/1.24 inference(backward_demodulation,[status(thm)],[f92,f323])).
% 1.34/1.24 thf(f323,plain,(
% 1.34/1.24 ($false = ('const/sets/IN' @ sK1 @ sK7 @ sK4)) | (~spl5_1 | ~spl5_4 | ~spl5_6)),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f322])).
% 1.34/1.24 thf(f322,plain,(
% 1.34/1.24 ($false = $true) | ($false = ('const/sets/IN' @ sK1 @ sK7 @ sK4)) | (~spl5_1 | ~spl5_4 | ~spl5_6)),
% 1.34/1.24 inference(forward_demodulation,[status(thm)],[f321,f87])).
% 1.34/1.24 thf(f87,plain,(
% 1.34/1.24 (('const/sets/IN' @ sK0 @ sK8 @ sK3) = $true) | ~spl5_6),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.34/1.24 thf(f85,definition,(
% 1.34/1.24 spl5_6 <=> (('const/sets/IN' @ sK0 @ sK8 @ sK3) = $true)),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.34/1.24 thf(f321,plain,(
% 1.34/1.24 (('const/sets/IN' @ sK0 @ sK8 @ sK3) = $false) | ($false = ('const/sets/IN' @ sK1 @ sK7 @ sK4)) | (~spl5_1 | ~spl5_4)),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f314])).
% 1.34/1.24 thf(f314,plain,(
% 1.34/1.24 ($false = $true) | ($false = ('const/sets/IN' @ sK1 @ sK7 @ sK4)) | (('const/sets/IN' @ sK0 @ sK8 @ sK3) = $false) | (~spl5_1 | ~spl5_4)),
% 1.34/1.24 inference(superposition,[status(thm)],[f77,f65])).
% 1.34/1.24 thf(f65,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X3 : sK0] : (((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X3 @ X2)) = $true) | (('const/sets/IN' @ sK0 @ X3 @ sK3) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK4))) ) | ~spl5_1),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.34/1.24 thf(f64,definition,(
% 1.34/1.24 spl5_1 <=> ! [X2 : sK1,X3 : sK0] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK4)) | (('const/sets/IN' @ sK0 @ X3 @ sK3) = $false) | ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X3 @ X2)) = $true))),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.34/1.24 thf(f77,plain,(
% 1.34/1.24 ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ sK8 @ sK7)) = $false) | ~spl5_4),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.34/1.24 thf(f75,definition,(
% 1.34/1.24 spl5_4 <=> ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ sK8 @ sK7)) = $false)),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.34/1.24 thf(f92,plain,(
% 1.34/1.24 (('const/sets/IN' @ sK1 @ sK7 @ sK4) = $true) | ~spl5_7),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.34/1.24 thf(f90,definition,(
% 1.34/1.24 spl5_7 <=> (('const/sets/IN' @ sK1 @ sK7 @ sK4) = $true)),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 1.34/1.24 thf(f308,plain,(
% 1.34/1.24 spl5_1 | ~spl5_2),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f300,f67,f64])).
% 1.34/1.24 thf(f67,definition,(
% 1.34/1.24 spl5_2 <=> ! [X1 : 'type/pair/prod' @ sK0 @ sK1] : (((sK2 @ X1) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $false))),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.34/1.24 thf(f300,plain,(
% 1.34/1.24 ( ! [X0 : sK0,X1 : sK1] : (((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X0 @ X1)) = $true) | ($false = ('const/sets/IN' @ sK0 @ X0 @ sK3)) | (('const/sets/IN' @ sK1 @ X1 @ sK4) = $false)) ) | ~spl5_2),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f292])).
% 1.34/1.24 thf(f292,plain,(
% 1.34/1.24 ( ! [X0 : sK0,X1 : sK1] : ((('const/sets/IN' @ sK1 @ X1 @ sK4) = $false) | ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X0 @ X1)) = $true) | ($false = ('const/sets/IN' @ sK0 @ X0 @ sK3)) | ($false = $true)) ) | ~spl5_2),
% 1.34/1.24 inference(superposition,[status(thm)],[f68,f49])).
% 1.34/1.24 thf(f49,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : ((('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5)) = $true) | (('const/sets/IN' @ X0 @ X2 @ X4) = $false) | (('const/sets/IN' @ X1 @ X3 @ X5) = $false)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.34/1.24 thf(f45,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : ((('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5)) = $true) | ($false = (('const/sets/IN' @ X0 @ X2 @ X4) & ('const/sets/IN' @ X1 @ X3 @ X5)))) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.34/1.24 thf(f16,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : ((('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5)) = (('const/sets/IN' @ X0 @ X2 @ X4) & ('const/sets/IN' @ X1 @ X3 @ X5)))) )),
% 1.34/1.24 inference(cnf_transformation,[status(thm)],[f7])).
% 1.34/1.24 thf(f7,plain,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5)) = (('const/sets/IN' @ X0 @ X2 @ X4) & ('const/sets/IN' @ X1 @ X3 @ X5)))),
% 1.34/1.24 inference(fool_elimination,[status(thm)],[f6])).
% 1.34/1.24 thf(f6,plain,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : (('const/sets/IN' @ X1 @ X3 @ X5) & ('const/sets/IN' @ X0 @ X2 @ X4) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5)))),
% 1.34/1.24 inference(rectify,[status(thm)],[f1])).
% 1.34/1.24 thf(f1,axiom,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X3 : X0,X4 : X1,X5 : X0 > $o,X6 : X1 > $o] : (('const/sets/IN' @ X1 @ X4 @ X6) & ('const/sets/IN' @ X0 @ X3 @ X5) = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X3 @ X4) @ ('const/sets/CROSS' @ X0 @ X1 @ X5 @ X6)))),
% 1.34/1.24 file('/export/starexec/sandbox2/tmp/tmp.UBNaezbv7d/DTF2THF_10777.p','thm/sets/IN_CROSS_')).
% 1.34/1.24 thf(f68,plain,(
% 1.34/1.24 ( ! [X1 : 'type/pair/prod' @ sK0 @ sK1] : ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $false) | ((sK2 @ X1) = $true)) ) | ~spl5_2),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.34/1.24 thf(f290,plain,(
% 1.34/1.24 ~spl5_1 | ~spl5_3 | ~spl5_5),
% 1.34/1.24 inference(avatar_contradiction_clause,[status(thm)],[f289])).
% 1.34/1.24 thf(f289,plain,(
% 1.34/1.24 $false | (~spl5_1 | ~spl5_3 | ~spl5_5)),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f288])).
% 1.34/1.24 thf(f288,plain,(
% 1.34/1.24 ($false = $true) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
% 1.34/1.24 inference(backward_demodulation,[status(thm)],[f82,f287])).
% 1.34/1.24 thf(f287,plain,(
% 1.34/1.24 ( ! [X0 : sK1 > $o] : ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ X0)) = $false)) ) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f286])).
% 1.34/1.24 thf(f286,plain,(
% 1.34/1.24 ( ! [X0 : sK1 > $o] : ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ X0)) = $false) | ($false = $true)) ) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
% 1.34/1.24 inference(forward_demodulation,[status(thm)],[f281,f73])).
% 1.34/1.24 thf(f73,plain,(
% 1.34/1.24 ($false = (sK2 @ sK6)) | ~spl5_3),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.34/1.24 thf(f71,definition,(
% 1.34/1.24 spl5_3 <=> ($false = (sK2 @ sK6))),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.34/1.24 thf(f281,plain,(
% 1.34/1.24 ( ! [X0 : sK1 > $o] : ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ X0)) = $false) | ((sK2 @ sK6) = $true)) ) | (~spl5_1 | ~spl5_5)),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f270])).
% 1.34/1.24 thf(f270,plain,(
% 1.34/1.24 ( ! [X0 : sK1 > $o] : (($false = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ X0)) = $false) | ((sK2 @ sK6) = $true)) ) | (~spl5_1 | ~spl5_5)),
% 1.34/1.24 inference(superposition,[status(thm)],[f82,f256])).
% 1.34/1.24 thf(f256,plain,(
% 1.34/1.24 ( ! [X2 : sK1 > $o,X0 : 'type/pair/prod' @ sK0 @ sK1,X1 : sK0 > $o] : (($false = ('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ X1 @ sK4))) | ((sK2 @ X0) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ X2)) = $false)) ) | ~spl5_1),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f252])).
% 1.34/1.24 thf(f252,plain,(
% 1.34/1.24 ( ! [X2 : sK1 > $o,X0 : 'type/pair/prod' @ sK0 @ sK1,X1 : sK0 > $o] : (((sK2 @ X0) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ X2)) = $false) | ($false = ('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ X1 @ sK4))) | ($false = $true)) ) | ~spl5_1),
% 1.34/1.24 inference(superposition,[status(thm)],[f250,f233])).
% 1.34/1.24 thf(f233,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X1 @ X0,X3 : X1 > $o,X4 : X0 > $o] : ((('const/sets/IN' @ X1 @ (sK10 @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (~ (X2 = Y0)))) @ X3) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ X1 @ X0 @ X2 @ ('const/sets/CROSS' @ X1 @ X0 @ X3 @ X4)) = $false)) )),
% 1.34/1.24 inference(superposition,[status(thm)],[f48,f115])).
% 1.34/1.24 thf(f115,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X1 @ X0] : ((('const/pair/,' @ X1 @ X0 @ (sK10 @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (~ (X2 = Y0)))) @ (sK9 @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (~ (X2 = Y0))))) = X2)) )),
% 1.34/1.24 inference(leibniz_equality_elimination,[status(thm)],[f57])).
% 1.34/1.24 thf(f57,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : 'type/pair/prod' @ X0 @ X1] : (((X2 @ ('const/pair/,' @ X0 @ X1 @ (sK10 @ X0 @ X1 @ X2) @ (sK9 @ X0 @ X1 @ X2))) = $false) | ((X2 @ X3) = $true)) )),
% 1.34/1.24 inference(pi_clausification,[status(thm)],[f56])).
% 1.34/1.24 thf(f56,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (((X2 @ ('const/pair/,' @ X0 @ X1 @ (sK10 @ X0 @ X1 @ X2) @ (sK9 @ X0 @ X1 @ X2))) = $false) | ((!! @ 'type/pair/prod' @ X0 @ X1 @ X2) = $true)) )),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.34/1.24 thf(f55,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (((!! @ 'type/pair/prod' @ X0 @ X1 @ X2) = $true) | (((^[Y0 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ (sK9 @ X0 @ X1 @ X2)))) @ (sK10 @ X0 @ X1 @ X2)) = $false)) )),
% 1.34/1.24 inference(sigma_clausification,[status(thm)],[f54])).
% 1.34/1.24 thf(f54,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (($false = (!! @ X0 @ (^[Y0 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y0 @ (sK9 @ X0 @ X1 @ X2)))))) | ((!! @ 'type/pair/prod' @ X0 @ X1 @ X2) = $true)) )),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.34/1.24 thf(f53,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : ((((^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0))))) @ (sK9 @ X0 @ X1 @ X2)) = $false) | ((!! @ 'type/pair/prod' @ X0 @ X1 @ X2) = $true)) )),
% 1.34/1.24 inference(sigma_clausification,[status(thm)],[f52])).
% 1.34/1.24 thf(f52,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0)))))) = $false) | ((!! @ 'type/pair/prod' @ X0 @ X1 @ X2) = $true)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.34/1.24 thf(f50,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0)))))) = (!! @ 'type/pair/prod' @ X0 @ X1 @ X2))) )),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.34/1.24 thf(f17,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0)))))) = (!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (X2 @ Y0))))) )),
% 1.34/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.34/1.24 thf(f11,plain,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : ((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0)))))) = (!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (X2 @ Y0))))),
% 1.34/1.24 inference(fool_elimination,[status(thm)],[f10])).
% 1.34/1.24 thf(f10,plain,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o] : (! [X3 : 'type/pair/prod' @ X0 @ X1] : (X2 @ X3) = ! [X4 : X0,X5 : X1] : (X2 @ ('const/pair/,' @ X0 @ X1 @ X4 @ X5)))),
% 1.34/1.24 inference(rectify,[status(thm)],[f2])).
% 1.34/1.24 thf(f2,axiom,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X7 : 'type/pair/prod' @ X0 @ X1 > $o] : (! [X3 : 'type/pair/prod' @ X0 @ X1] : (X7 @ X3) = ! [X3 : X0,X4 : X1] : (X7 @ ('const/pair/,' @ X0 @ X1 @ X3 @ X4)))),
% 1.34/1.24 file('/export/starexec/sandbox2/tmp/tmp.UBNaezbv7d/DTF2THF_10777.p','thm/pair/FORALL_PAIR_THM_')).
% 1.34/1.24 thf(f48,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : (($false = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5))) | (('const/sets/IN' @ X0 @ X2 @ X4) = $true)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.34/1.24 thf(f46,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : (((('const/sets/IN' @ X0 @ X2 @ X4) & ('const/sets/IN' @ X1 @ X3 @ X5)) = $true) | ($false = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5)))) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.34/1.24 thf(f250,plain,(
% 1.34/1.24 ( ! [X0 : 'type/pair/prod' @ sK0 @ sK1,X1 : sK0 > $o] : ((('const/sets/IN' @ sK0 @ (sK10 @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (~ (X0 = Y0)))) @ sK3) = $false) | ((sK2 @ X0) = $true) | ($false = ('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ X1 @ sK4)))) ) | ~spl5_1),
% 1.34/1.24 inference(trivial_inequality_removal,[status(thm)],[f247])).
% 1.34/1.24 thf(f247,plain,(
% 1.34/1.24 ( ! [X0 : 'type/pair/prod' @ sK0 @ sK1,X1 : sK0 > $o] : (($false = ('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ X1 @ sK4))) | (('const/sets/IN' @ sK0 @ (sK10 @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (~ (X0 = Y0)))) @ sK3) = $false) | ($false = $true) | ((sK2 @ X0) = $true)) ) | ~spl5_1),
% 1.34/1.24 inference(superposition,[status(thm)],[f234,f239])).
% 1.34/1.24 thf(f239,plain,(
% 1.34/1.24 ( ! [X0 : 'type/pair/prod' @ sK0 @ sK1] : ((('const/sets/IN' @ sK1 @ (sK9 @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (~ (X0 = Y0)))) @ sK4) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (~ (X0 = Y0)))) @ sK3) = $false) | ((sK2 @ X0) = $true)) ) | ~spl5_1),
% 1.34/1.24 inference(superposition,[status(thm)],[f65,f115])).
% 1.34/1.24 thf(f234,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/pair/prod' @ X1 @ X0,X3 : X1 > $o,X4 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK9 @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (~ (X2 = Y0)))) @ X4) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ X1 @ X0 @ X2 @ ('const/sets/CROSS' @ X1 @ X0 @ X3 @ X4)) = $false)) )),
% 1.34/1.24 inference(superposition,[status(thm)],[f47,f115])).
% 1.34/1.24 thf(f47,plain,(
% 1.34/1.24 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0 > $o,X5 : X1 > $o] : (($false = ('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ ('const/pair/,' @ X0 @ X1 @ X2 @ X3) @ ('const/sets/CROSS' @ X0 @ X1 @ X4 @ X5))) | (('const/sets/IN' @ X1 @ X3 @ X5) = $true)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.34/1.24 thf(f82,plain,(
% 1.34/1.24 (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $true) | ~spl5_5),
% 1.34/1.24 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.34/1.24 thf(f80,definition,(
% 1.34/1.24 spl5_5 <=> (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $true)),
% 1.34/1.24 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.34/1.24 thf(f95,plain,(
% 1.34/1.24 spl5_5 | spl5_7),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f31,f90,f80])).
% 1.34/1.24 thf(f31,plain,(
% 1.34/1.24 (('const/sets/IN' @ sK1 @ sK7 @ sK4) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.34/1.24 thf(f29,plain,(
% 1.34/1.24 ((('const/sets/IN' @ sK1 @ sK7 @ sK4) & ('const/sets/IN' @ sK0 @ sK8 @ sK3)) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.34/1.24 thf(f27,plain,(
% 1.34/1.24 ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false) | ((('const/sets/IN' @ sK1 @ sK7 @ sK4) & ('const/sets/IN' @ sK0 @ sK8 @ sK3)) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.34/1.24 thf(f25,plain,(
% 1.34/1.24 (((('const/sets/IN' @ sK1 @ sK7 @ sK4) & ('const/sets/IN' @ sK0 @ sK8 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ sK8 @ sK7))) = $false) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false)),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.34/1.24 thf(f24,plain,(
% 1.34/1.24 (((^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ sK7 @ sK4) & ('const/sets/IN' @ sK0 @ Y0 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y0 @ sK7)))) @ sK8) = $false) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false)),
% 1.34/1.24 inference(sigma_clausification,[status(thm)],[f23])).
% 1.34/1.24 thf(f23,plain,(
% 1.34/1.24 ((!! @ sK0 @ (^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ sK7 @ sK4) & ('const/sets/IN' @ sK0 @ Y0 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y0 @ sK7))))) = $false) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false)),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.34/1.24 thf(f22,plain,(
% 1.34/1.24 (((^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0)))))) @ sK7) = $false) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false)),
% 1.34/1.24 inference(sigma_clausification,[status(thm)],[f21])).
% 1.34/1.24 thf(f21,plain,(
% 1.34/1.24 ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) = $false) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false)),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.34/1.24 thf(f20,plain,(
% 1.34/1.24 (((^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0))) @ sK6) = $false) | ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) = $false)),
% 1.34/1.24 inference(sigma_clausification,[status(thm)],[f19])).
% 1.34/1.24 thf(f19,plain,(
% 1.34/1.24 ($false = (!! @ 'type/pair/prod' @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0))))) | ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) = $false)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.34/1.24 thf(f15,plain,(
% 1.34/1.24 ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) != (!! @ 'type/pair/prod' @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0)))))),
% 1.34/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.34/1.24 thf(f14,plain,(
% 1.34/1.24 ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) != (!! @ 'type/pair/prod' @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0)))))),
% 1.34/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f12,f13])).
% 1.34/1.24 thf(f13,plain,(
% 1.34/1.24 ? [X0 : $tType,X1 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : X0 > $o,X4 : X1 > $o] : ((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: ((('const/sets/IN' @ X1 @ Y0 @ X4) & ('const/sets/IN' @ X0 @ Y1 @ X3)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0))))))) != (!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ Y0))))) => ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) != (!! @ 'type/pair/prod' @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0)))))),
% 1.34/1.24 introduced(definition,[],[choice_axiom])).
% 1.34/1.24 thf(f12,plain,(
% 1.34/1.24 ? [X0 : $tType,X1 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : X0 > $o,X4 : X1 > $o] : ((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: ((('const/sets/IN' @ X1 @ Y0 @ X4) & ('const/sets/IN' @ X0 @ Y1 @ X3)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0))))))) != (!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ Y0)))))),
% 1.34/1.24 inference(ennf_transformation,[status(thm)],[f9])).
% 1.34/1.24 thf(f9,plain,(
% 1.34/1.24 ~! [X0 : $tType,X1 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : X0 > $o,X4 : X1 > $o] : ((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: ((('const/sets/IN' @ X1 @ Y0 @ X4) & ('const/sets/IN' @ X0 @ Y1 @ X3)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ Y1 @ Y0))))))) = (!! @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ Y0)))))),
% 1.34/1.24 inference(fool_elimination,[status(thm)],[f8])).
% 1.34/1.24 thf(f8,plain,(
% 1.34/1.24 ~! [X0 : $tType,X1 : $tType,X2 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : X0 > $o,X4 : X1 > $o] : (! [X5 : 'type/pair/prod' @ X0 @ X1] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ X5 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X2 @ X5)) = ! [X6 : X0,X7 : X1] : ((('const/sets/IN' @ X0 @ X6 @ X3) & ('const/sets/IN' @ X1 @ X7 @ X4)) => (X2 @ ('const/pair/,' @ X0 @ X1 @ X6 @ X7))))),
% 1.34/1.24 inference(rectify,[status(thm)],[f4])).
% 1.34/1.24 thf(f4,negated_conjecture,(
% 1.34/1.24 ~! [X0 : $tType,X1 : $tType,X7 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : X0 > $o,X4 : X1 > $o] : (! [X5 : 'type/pair/prod' @ X0 @ X1] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ X5 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X7 @ X5)) = ! [X5 : X0,X6 : X1] : ((('const/sets/IN' @ X0 @ X5 @ X3) & ('const/sets/IN' @ X1 @ X6 @ X4)) => (X7 @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6))))),
% 1.34/1.24 inference(negated_conjecture,[status(cth)],[f3])).
% 1.34/1.24 thf(f3,conjecture,(
% 1.34/1.24 ! [X0 : $tType,X1 : $tType,X7 : 'type/pair/prod' @ X0 @ X1 > $o,X3 : X0 > $o,X4 : X1 > $o] : (! [X5 : 'type/pair/prod' @ X0 @ X1] : (('const/sets/IN' @ 'type/pair/prod' @ X0 @ X1 @ X5 @ ('const/sets/CROSS' @ X0 @ X1 @ X3 @ X4)) => (X7 @ X5)) = ! [X5 : X0,X6 : X1] : ((('const/sets/IN' @ X0 @ X5 @ X3) & ('const/sets/IN' @ X1 @ X6 @ X4)) => (X7 @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6))))),
% 1.34/1.24 file('/export/starexec/sandbox2/tmp/tmp.UBNaezbv7d/DTF2THF_10777.p','thm/sets/FORALL_IN_CROSS_')).
% 1.34/1.24 thf(f94,plain,(
% 1.34/1.24 spl5_5 | spl5_6),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f30,f85,f80])).
% 1.34/1.24 thf(f30,plain,(
% 1.34/1.24 (('const/sets/IN' @ sK0 @ sK8 @ sK3) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.34/1.24 thf(f93,plain,(
% 1.34/1.24 spl5_7 | spl5_3),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f33,f71,f90])).
% 1.34/1.24 thf(f33,plain,(
% 1.34/1.24 ($false = (sK2 @ sK6)) | (('const/sets/IN' @ sK1 @ sK7 @ sK4) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.34/1.24 thf(f28,plain,(
% 1.34/1.24 ($false = (sK2 @ sK6)) | ((('const/sets/IN' @ sK1 @ sK7 @ sK4) & ('const/sets/IN' @ sK0 @ sK8 @ sK3)) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.34/1.24 thf(f88,plain,(
% 1.34/1.24 spl5_3 | spl5_6),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f32,f85,f71])).
% 1.34/1.24 thf(f32,plain,(
% 1.34/1.24 ($false = (sK2 @ sK6)) | (('const/sets/IN' @ sK0 @ sK8 @ sK3) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.34/1.24 thf(f83,plain,(
% 1.34/1.24 spl5_4 | spl5_5),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f35,f80,f75])).
% 1.34/1.24 thf(f35,plain,(
% 1.34/1.24 ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ sK8 @ sK7)) = $false) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.34/1.24 thf(f26,plain,(
% 1.34/1.24 ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ sK6 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ sK6)) = $false) | ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ sK8 @ sK7)) = $false)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.34/1.24 thf(f78,plain,(
% 1.34/1.24 spl5_3 | spl5_4),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f34,f75,f71])).
% 1.34/1.24 thf(f34,plain,(
% 1.34/1.24 ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ sK8 @ sK7)) = $false) | ($false = (sK2 @ sK6))),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.34/1.24 thf(f69,plain,(
% 1.34/1.24 spl5_1 | spl5_2),
% 1.34/1.24 inference(avatar_split_clause,[status(thm)],[f44,f67,f64])).
% 1.34/1.24 thf(f44,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X3 : sK0,X1 : 'type/pair/prod' @ sK0 @ sK1] : (((sK2 @ X1) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK4)) | ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X3 @ X2)) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $false) | (('const/sets/IN' @ sK0 @ X3 @ sK3) = $false)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.34/1.24 thf(f43,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X3 : sK0,X1 : 'type/pair/prod' @ sK0 @ sK1] : (((('const/sets/IN' @ sK1 @ X2 @ sK4) & ('const/sets/IN' @ sK0 @ X3 @ sK3)) = $false) | ((sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X3 @ X2)) = $true) | ((sK2 @ X1) = $true) | (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $false)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.34/1.24 thf(f42,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X3 : sK0,X1 : 'type/pair/prod' @ sK0 @ sK1] : ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) = $false) | ($true = ((('const/sets/IN' @ sK1 @ X2 @ sK4) & ('const/sets/IN' @ sK0 @ X3 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X3 @ X2)))) | ((sK2 @ X1) = $true)) )),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.34/1.24 thf(f41,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X3 : sK0,X1 : 'type/pair/prod' @ sK0 @ sK1] : (((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ X1)) = $true) | ($true = ((('const/sets/IN' @ sK1 @ X2 @ sK4) & ('const/sets/IN' @ sK0 @ X3 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ X3 @ X2))))) )),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.34/1.24 thf(f40,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X3 : sK0,X1 : 'type/pair/prod' @ sK0 @ sK1] : ((((^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ X2 @ sK4) & ('const/sets/IN' @ sK0 @ Y0 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y0 @ X2)))) @ X3) = $true) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ X1)) = $true)) )),
% 1.34/1.24 inference(pi_clausification,[status(thm)],[f39])).
% 1.34/1.24 thf(f39,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X1 : 'type/pair/prod' @ sK0 @ sK1] : (((!! @ sK0 @ (^[Y0 : sK0]: ((('const/sets/IN' @ sK1 @ X2 @ sK4) & ('const/sets/IN' @ sK0 @ Y0 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y0 @ X2))))) = $true) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ X1)) = $true)) )),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.34/1.24 thf(f38,plain,(
% 1.34/1.24 ( ! [X2 : sK1,X1 : 'type/pair/prod' @ sK0 @ sK1] : (((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ X1)) = $true) | (((^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0)))))) @ X2) = $true)) )),
% 1.34/1.24 inference(pi_clausification,[status(thm)],[f37])).
% 1.34/1.24 thf(f37,plain,(
% 1.34/1.24 ( ! [X1 : 'type/pair/prod' @ sK0 @ sK1] : (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) = $true) | ((('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ X1 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ X1)) = $true)) )),
% 1.34/1.24 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.34/1.24 thf(f36,plain,(
% 1.34/1.24 ( ! [X1 : 'type/pair/prod' @ sK0 @ sK1] : ((((^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0))) @ X1) = $true) | ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) = $true)) )),
% 1.34/1.24 inference(pi_clausification,[status(thm)],[f18])).
% 1.34/1.24 thf(f18,plain,(
% 1.34/1.24 ((!! @ 'type/pair/prod' @ sK0 @ sK1 @ (^[Y0 : 'type/pair/prod' @ sK0 @ sK1]: (('const/sets/IN' @ 'type/pair/prod' @ sK0 @ sK1 @ Y0 @ ('const/sets/CROSS' @ sK0 @ sK1 @ sK3 @ sK4)) => (sK2 @ Y0)))) = $true) | ((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/sets/IN' @ sK1 @ Y0 @ sK4) & ('const/sets/IN' @ sK0 @ Y1 @ sK3)) => (sK2 @ ('const/pair/,' @ sK0 @ sK1 @ Y1 @ Y0))))))) = $true)),
% 1.34/1.24 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.34/1.24 % SZS output end Proof for DTF2THF_10777
% 1.34/1.24 % (10904)------------------------------
% 1.34/1.24 % (10904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.24 % (10904)Termination reason: Refutation
% 1.34/1.24
% 1.34/1.24 % (10904)Memory used [KB]: 5884
% 1.34/1.24 % (10904)Time elapsed: 0.044 s
% 1.34/1.24 % (10904)Instructions burned: 77 (million)
% 1.34/1.24 % (10904)------------------------------
% 1.34/1.24 % (10904)------------------------------
% 1.34/1.24 % (10874)Success in time 0.143 s
%------------------------------------------------------------------------------